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Simplifying 5x2 + -1x + -115 = 0 Reorder the terms: -115 + -1x + 5x2 = 0 Solving -115 + -1x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -23 + -0.2x + x2 = 0 Move the constant term to the right: Add '23' to each side of the equation. -23 + -0.2x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + -0.2x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -0.2x + x2 = 0 + 23 -0.2x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 -0.2x + x2 = 23 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = 23 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 23 + 0.01 Combine like terms: 23 + 0.01 = 23.01 0.01 + -0.2x + x2 = 23.01 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 23.01 Calculate the square root of the right side: 4.796873982 Break this problem into two subproblems by setting (x + -0.1) equal to 4.796873982 and -4.796873982.Subproblem 1
x + -0.1 = 4.796873982 Simplifying x + -0.1 = 4.796873982 Reorder the terms: -0.1 + x = 4.796873982 Solving -0.1 + x = 4.796873982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 4.796873982 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 4.796873982 + 0.1 x = 4.796873982 + 0.1 Combine like terms: 4.796873982 + 0.1 = 4.896873982 x = 4.896873982 Simplifying x = 4.896873982Subproblem 2
x + -0.1 = -4.796873982 Simplifying x + -0.1 = -4.796873982 Reorder the terms: -0.1 + x = -4.796873982 Solving -0.1 + x = -4.796873982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -4.796873982 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -4.796873982 + 0.1 x = -4.796873982 + 0.1 Combine like terms: -4.796873982 + 0.1 = -4.696873982 x = -4.696873982 Simplifying x = -4.696873982Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.896873982, -4.696873982}
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